Coefficient, Variable, and Constant

• A Variable is a symbol for a number we don't know yet. It is usually a letter like x or y
• A Coefficient is a number used to multiply a variable, \(8x\) means \(8\) times \(x\), so \(8\) is a coefficient
• A Constant is a number on its own

\begin{array}{cccc} \huge \color{blue} -2x^3  && \huge \color{blue} + &&\huge \color {blue} 5\\\\ 1^{\text{st}} \text{ term} && && 2^{\text{nd}} \text{ term}\\ \text{Coefficient : −2}&& &&\text{5 called constant}\\ \text{Exponent of variable : 3}&& &&\text{Exponent of variable : 0} \end{array}

Polynomial

Monomial → The special names for polynomials with 1 term.

Example: \( 3xy^2,\: 2x^5,\: 4y, \:5x\)

Binomial → The special names for polynomials with 2 terms.

Example: \(7x - 2, \:8x^2 - 3y, \:2x - 4y^2, \:9a - b^4\)

Trinomial → The special names for polynomials with 3 terms.

Example: \( 2x^2 + 3y - 5z, \:5a^2 + b + c^2, \: 3i - 2j + 5k\)

Expressing mathematical relationships algebraically

Example:

Write down an algebraic expression the following statements.

• Subtract twice the variable x from the product of 2x and y
• Multiply the square of y by 2x
• Add the cube root of the product of x and y to 4a

Solution:

• \( 2xy - 2x\)
• \(2xy^2\)
• \(\sqrt[3]{xy} + 4a\)